In a skillet, heat oil over medium-high. Soften tortillas in the hot oil 30 seconds per side. Drain on paper towel; cool.
In a large saucepan, melt butter over medium heat. Blend in flour. Whisk in chicken broth, cook and stir until thickened. Remove from the heat. Stir in sour cream and taco sauce. Keep warm but do not boil. Divide the chicken, 2-1/2 cups Monterey Jack cheese and all but 2 tablespoons of the onions over the 12 tortillas. Arrange asparagus over filling with the tips extending beyond the tortillas. Top each with 2 tablespoons sauce. Roll up and arrange, seam side down, in a 13x9-in. baking dish. Top with reserved sauce and the Parmesan cheese.
Bake at 400° for 25 minutes or until bubbly. Sprinkle with remaining Monterey Jack cheese and return to the oven just until melted. Garnish with olives and reserved onions. Serve with additional green taco sauce.